Publications

Order by: publication date number of citations

• xSPDE3: Extensible software for stochastic ordinary and partial differential equations

  Simon Kiesewetter, Ria R. Joseph, Peter D. Drummond

  SciPost Phys. Codebases 17 (2023) · published 2 October 2023 | Toggle abstract · pdf

  The xSPDE toolbox treats stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and/or sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. All equations may have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector field component, and at either end of any interval.

  1 citation

• Codebase release 3.44 for xSPDE

  Simon Kiesewetter, Ria R. Joseph, Peter D. Drummond

  SciPost Phys. Codebases 17-r3.44 (2023) · published 2 October 2023 | Toggle abstract · src

  The xSPDE toolbox treats stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and/or sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. All equations may have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector field component, and at either end of any interval.

  1 citation

• Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

  Andy Chia, Wai-Keong (Dariel) Mok, Changsuk Noh, Leong-Chuan Kwek

  SciPost Phys. 15, 121 (2023) · published 28 September 2023 | Toggle abstract · pdf

  It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

• Maximum entanglement of mixed symmetric states under unitary transformations

  Eduardo Serrano-Ensástiga, John Martin

  SciPost Phys. 15, 120 (2023) · published 28 September 2023 | Toggle abstract · pdf

  We study the maximum entanglement that can be produced by a global unitary transformation for systems of two and three qubits constrained to the fully symmetric states. This restriction to the symmetric subspace appears naturally in the context of bosonic or collective spin systems. We also study the symmetric states that remain separable after any global unitary transformation, called symmetric absolutely separable (SAS) states, or absolutely classical for spin states. The results for the two-qubit system are deduced analytically. In particular, we determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that contains the set of SAS states. As an application of our results, we also analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. For the symmetric three-qubit case, our results are mostly numerical, and we conjecture a 3-parameter family of states that achieves the maximum negativity in the unitary orbit of any mixed state. In addition, we derive upper bounds, apparently tight, on the radii of balls containing only/all SAS states.

  1 citation

• A time-dependent regularization of the Redfield equation

  Antonio D'Abbruzzo, Vasco Cavina, Vittorio Giovannetti

  SciPost Phys. 15, 117 (2023) · published 27 September 2023 | Toggle abstract · pdf

  We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive divisible quantum process. Using the dynamics of an exactly-solvable three-level open system as a reference, we show that our approach performs better during the transient evolution, if compared to other approaches like the partial secular master equation or the universal Lindblad equation. To make the comparison between different regularization schemes independent from the initial state, we introduce a new quantitative approach based on the Choi-Jamiołkowski isomorphism.

• First-order photon condensation in magnetic cavities: A two-leg ladder model

  Zeno Bacciconi, Gian M. Andolina, Titas Chanda, Giuliano Chiriacò, Marco Schirò, Marcello Dalmonte

  SciPost Phys. 15, 113 (2023) · published 25 September 2023 | Toggle abstract · pdf

  We consider a model of free fermions in a ladder geometry coupled to a non-uniform cavity mode via Peierls substitution. Since the cavity mode generates a magnetic field, no-go theorems on spontaneous photon condensation do not apply, and we indeed observe a phase transition to a photon condensed phase characterized by finite circulating currents, alternatively referred to as the equilibrium superradiant phase. We consider both square and triangular ladder geometries, and characterize the transition by studying the energy structure of the system, light-matter entanglement, the properties of the photon mode, and chiral currents. The transition is of first order and corresponds to a sudden change in the fermionic band structure as well as the number of its Fermi points. Thanks to the quasi-one dimensional geometry we scrutinize the accuracy of (mean field) cavity-matter decoupling against large scale density-matrix renormalization group simulations. We find that light-matter entanglement is essential for capturing corrections to matter properties at finite sizes and for the description of the correct photon state. The latter remains Gaussian in the the thermodynamic limit both in the normal and photon condensed phases.

  4 citations

• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

  João C. Getelina, Niladri Gomes, Thomas Iadecola, Peter P. Orth, Yong-Xin Yao

  SciPost Phys. 15, 102 (2023) · published 19 September 2023 | Toggle abstract · pdf

  Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

  5 citations

• Projective cluster-additive transformation for quantum lattice models

  Max Hörmann, Kai P. Schmidt

  SciPost Phys. 15, 097 (2023) · published 15 September 2023 | Toggle abstract · pdf

  We construct a projection-based cluster-additive transformation that block-diagonalizes wide classes of lattice Hamiltonians $\mathcal{H}=\mathcal{H}_0 +V$. Its cluster additivity is an essential ingredient to set up perturbative or non-perturbative linked-cluster expansions for degenerate excitation subspaces of $\mathcal{H}_0$. Our transformation generalizes the minimal transformation known amongst others under the names Takahashi's transformation, Schrieffer-Wolff transformation, des Cloiseaux effective Hamiltonian, canonical van Vleck effective Hamiltonian or two-block orthogonalization method. The effective cluster-additive Hamiltonian and the transformation for a given subspace of $\mathcal{H}$, that is adiabatically connected to the eigenspace of $\mathcal{H}_0$ with eigenvalue $e_0^n$, solely depends on the eigenspaces of $\mathcal{H}$ connected to $e_0^m$ with $e_0^m≤ e_0^n$. In contrast, other cluster-additive transformations like the multi-block orthogonalization method or perturbative continuous unitary transformations need a larger basis. This can be exploited to implement the transformation efficiently both perturbatively and non-perturbatively. As a benchmark, we perform perturbative and non-perturbative linked-cluster expansions in the low-field ordered phase of the transverse-field Ising model on the square lattice for single spin-flips and two spin-flip bound-states.

  1 citation

• Entanglement classification via operator size

  Qi-Feng Wu

  SciPost Phys. Core 6, 063 (2023) · published 15 September 2023 | Toggle abstract · pdf

  In this work, multipartite entanglement is classified by polynomials. I show that the operator size is closely related to the entanglement structure. Given a generic quantum state, I define a series of subspaces generated by operators of different sizes acting on it. The information about the entanglement is encoded into these subspaces. With the dimension of these subspaces as coefficients, I define a polynomial which I call the entanglement polynomial. The entanglement polynomial induces a homomorphism from quantum states to polynomials. It implies that we can characterize and find the building blocks of entanglement by polynomial factorization. Two states share the same entanglement polynomial if they are equivalent under the stochastic local operations and classical communication. To calculate the entanglement polynomial practically, I construct a series of states, called renormalized states, whose ranks are related to the coefficients of the entanglement polynomial.

• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain

  Emanuele Tirrito, Alessandro Santini, Rosario Fazio, Mario Collura

  SciPost Phys. 15, 096 (2023) · published 14 September 2023 | Toggle abstract · pdf

  Non-equilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce different non-equilibrium regimes and an abrupt change in the scaling-law of the bipartite entanglement entropy. However, our understanding of how these regimes appear{, how they affect the statistics of local quantities and}, finally whether they survive in the thermodynamic limit, is much less established. Here we investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment. In particular we show that local projective measurements induce a quantitative modification of the out-of-equilibrium probability distribution function of the local magnetization. Starting from a GHZ state, the relaxation of the paramagnetic and the ferromagnetic order is analysed. In particular we describe how the probability distributions associated to them show different behaviour depending on the measurement rate.

  13 citations